Question

1. According to the Guinness Book of World Records, the longest recorded paper-link chain was 6,077 ft long and was made by the first- and second-grade children at Rose City Elementary School, Indiana. If there are 8 paper links per foot, and it takes 1 minute to construct each link, estimate the length of time necessary to build this paper-link chain? (Round your answer to one decimal place.)

2. A history teacher gives a 17-question true-false exam. In how many ways can the test be answered if the possible answers are T or F or possibly to leave the answer blank?

3. How many three-digit numbers can be formed using the numerals {3, 4, 5, 6, 7, 8} without repetition?

4. What is the number of distinguishable arrangements of the letters in the word KARL?

5. A certain manufacturing process calls for the mixing of five chemicals. One liquid is to be poured into the vat, and then the others are to be added in turn. All possibilities must be tested to see which gives the best results. How many tests are required?

Answer #1

1) The number of minutes required is 6077*8*1 = 48616 minutes

2) Number of questions =17 and No of options = 3 (True , False and Blank)

Each question can be answered in 3 ways. Hence total number of
ways = 3^{17}

3) Numbers are to be formed from 3,4,5,6,7,8 without repetition

Let this number be XXX

For the units place you have 6 options

For the tens place you have 5 options (as there can be no repetition of the number in the units place)

For the hundredth place you have 4 options

Total numbers possible = 6*5*4 = 120

4) The letters available are K A R and L. These can be arranged amongst themselves in 4 factorial ways = 4*3*2 = 24 ways.

5) Again 5 chemicals can be arranged in 5 factorial ways = 5*4*3*2*1 = 120 ways. Hence total 120 tests are required.

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